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6/01 c:/CIRC/DateDue.p65-p. 15

 

 
Tae Study of a Two Phase Alternator with
@ Special Rotor

A Thesis Submitted to

The faculty of

MICHIGAN AGRICULTURAL COLLEGE

bo
-~ . a :
\

C. C. White

t

w. E. Thomas
Candidates for the Degree of

Bachelor of Science

September 12, 1919
THESis
139

(ou

THS
BIBLIOGRAPZY

Alternating currents
Magms son.

396 =~ 432 12—22

Theory of Electric Circuits.
Steinmetz

161-165

Electricity%and “liagnetism for Engineers
Pender

196-212

Alternating Surrent Wachines
Sheldon, Hason and Hausmam

18=24

PBoceedings of the American Institute of Electrical Engineers
Vol. XXXVITII Noe 8 Ang. 1919

947~958

Alternating Current ~lectricity
TMmbie & Higbie

Course II.

390-396

104079
| PRSFACE

Te subject of this thesis is the modification of a three phase, 220
volt, industion motor, into a two phase generator. In this two phase
generator we propose to put a rotor of special design and make a study of
the conditions that exist under the different shapes of pole faces and
types of rotors,

With this peculiar design we are endeavoring to build an alternator
that will supply a ture sine wave. Many alternators are built to supply
such a wave but when entering into the commercial field many of these
features have been sacrificed. They approach the sine wave, but due to
the fact that it is almost impossible to eliminate all of the odd harmonics
and the effect of the fringing of the field flux a slight deviation from
the sine curve has been the result.

It is our aim to take precautionary measures to eliminate as many of
the harmonics as we can by changing the shape of the pole faces, thus eli-
minating the fringing of the field flux as moh as possible, and get as
near to a true sine wave as we can. Then we aim as far as possible to
obtain a fair capacity from the machine so as tests may be run and have
students become familiar with two phase machinery.

we wish to thank the Kleotrical and Mechanical Departments for the
help they gave us while we were at work on this machines, also to

Mr. Wyckoff for the help rendered in work on the Oscillograph.
"WHE STUDY OF A TWO PHASE ALTERNATOR WITH A SPECIAL ROTOR"

We will not enter into the construction of the rotor as it is ad-
equately described in the detail and assemby drawings as is shown in
figures 4, 5, 6, 7, 8 9, 10 and ll. The materials used for the pole
pieces is cast iron and the shaft is made of cold roll steed,

The whole rotor was assembled and balanced to eliminate vibration.
The pole pieces were not made any particular shape only as a portion of
the true aro, this was done to see the action of the different shapes of
pole pieces on the form of the wave that would be generated.

fhe coll that we used was just an experimental coil. It is wound
with No. 20 double cotton covered copper wire. The dimensions are as in
(Pig. 8). The leads from the coil are brought out md soldered to the
collector rings that are shown in Fig. 9. We did not design the coil,
but merely used the space that we had to insert it and built a coil to

fit this space.

RE-CONNECTING THE STATOR.

The stator of this machine when operating as a three-phase, induction
motor was connected as a four pole, three phase parallel star, (Mig. 1-1).
This gave us a full pitch winding with four coils per pole per phase, or
a total of 468 slots. Because of this condition we were able to re-connect
it into a two phase machine. In the Electric Journal, Vol. 15, page 85,
enough data was obtained to aid us in this re-connection, first studying
the three phase comections, then making the changes 80 as to have it con-
nected as a two phase, four pole, series delta. In order to do this it
Was necessary for us to connect six coils in series instead of four.

We also referred to the thesis of W. & Siefert and H. G. Carrow; "A Study

Of Reconnection Induction Motors".
 

 
 

 

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Reactance Curve

 
2

After we finished the rotor and had the brushes in place, we assembled
the alternator and belted it to a 7 H.P. D.C. motor which served as a prime
mover. We ran preliminary tests to find out what work the machine was doing.
We found that the machine would generate alternating current and that the
ourrent was ninety degrees apart or two phase current. The next thing to
determine was the shape of the wave, so we connected a non-inductive load
thru an ammeter with a voltmeter at the terminals of the machine to see
what effect a load would have, each phase being loaded equally.

In running this test we found that we could not load the machine up
to the load we expected and when the wave form was obtained thru the oacillo-
graph many interesting things became evident. Without load the alternator
gave a Very g00d wave but as the load was applied it was distorted. ‘the
harmonics that we tried to eliminate came in so strong that they could be
determined on the screen. We also found that as the load was applied the
voltage on the machine dropped down, the speed of the machine remaining
constant. The field excitation remaining constant. With these conditions
in view we ran the following test to see if we could determine the cause
of this voltage drop.

Te First was the magnetization test, (See Curve of fig. 12).

Regulation test was made as follows: The armature was short oircuited
thru an ammeter. fhen the generator brought up td synchronous speed with-
out any field excitation. Ourrent was then passed thru the field and a
series of readings taxen of the field and the corresponding armature
currents until the armature current readings reached about 50% above the
normal full load value. From the magnetization curve, voltages corres-
ponding to the field current readings can be obtained. The curve was
plotted as on Mg. 12. Then with armature currents as abscissa and
terminal voltages corresponding to the field currents as ordinates the

curve was plotted (Fig. 13). The curve is nearly a straight line droop-
5 .
ing as the saturation point is appreached. After performing these tests
we were convinced that the voltage drop was due to synchronous reactance.
Both armature reaction and reactance are proportional in magnitude to the
current, the voltage consuméd by both are in phase for all power factors.
Both may be represented by one equivalent reactance. This is called
synchronous reactance.

The voltage consumed by the synchronous reactance is practically equal
to the total voltage as the part taken by the resistance is small and al-
most in phase with the induced voltage.

From the synchronous reactance curve, (Hig. 13):

E, * 1s R* + sXa* or
sXa = E, le

sXa = synchronous reactance,
Eo = Terminal volts.

1, = Armature current.
R " " Resistance.

The value obtained for the synchronous reactance is much larger than
actual asynchronous reactance when operating under full load. The syn-
chronous impedence and reactance varied with the load. It is important
that we know the synchronous reactance when studying the characteristics
of an alternator. The calculated regulation is only an approximation of
the actual value. In many altemators from 10 to 25% of the total syn-
chronous reactance is due to the armature reactance and this in turn is
due to the armature reaction.

As in Fig. 15, the flux is pushed down from, say a north pole to the
south pole by the synchronous reactance this is another theory of the
dropping of the voltage which is due to the synchronous reactance. The
flux should pass over the small air gap into the stator iron and tims

around and back thru the south pole, but instead of doing this it is
4

distorted and pushed straight down to the south pole as in Wig. 15. If
the flux is driven down in this mamer the number of lines cut is reduced
and the voltage will drop. These characteristics seem to be evident in
this case and as the load is applied the current rises and the syn-
Chronous readtance increases and the voltage drops. Therefore, the volt-
age drop mst be due to this reaction. We rana test to find out if the
voltage drop was due to the decreasing speed and found that the speed of .
the alternator was practically constant. Then the reactance will distort
the field flux so that it leaxs up thru the teeth rather than threading
thru the armature coils and in this manner the flux density would be re-
duced and thus cause a drop in voltage. It does not seem possible with
@ non-inductive load that the armature reaction would have a demagnetizing
effect, this would be true, however, if the load was an inductive one.

As is stated before the pole faces were that of a pure aro, and when
the picture of the current in the wire was taken with the oseillograph,
we found the wave form to be distorted as is shown in Fig. 14. The
general trend of the curve is that of a sine wave but when ahalyzing the
curve we find that the third harmonic is present. The portion that is
designated in Mg. 14 by the pointe (a) and (b) show the distorted portion
of the curve. This curve is the resultant of the third harmonic and the
fundamental combination of the both gives us the peculiar shape. Note
the amplitude of the higher harmonics as pointed out by point (b) Ne. 14,
the higher harmonics begin at the zero point and gradually inorease until
at the point (b), then decrease to the zero point again and then repeats
itself only in the negative direction.

In any circuit the first source of disturbance or distortion is in the
alternator. with no current flowing, which is a condition of an open
circuit, the voltage at the alternator terminals is proportional to the

rate of cutting the lines of force. In the case of an altermator it is
 
5
instantaneous values. Distortions may therefore be caused by the follow-
ing reasons:
1. Non-uniform or a pulsatine field.
2 Variation in speed.
3. The distribution of the oonductoss in which the
current is generated.

In our case the speed was constant so the distortion was not due to
this condition. There are a number of turns per coil and the coils fill
the six adjacent slots and might be the cause we have no way of finding
out only by making experiments on the different distribution of the con-
ductors. It may be that the field flux is not distributed uniformly due
to the quality of the cast iron and the shape of the pole faces, Then
the slotted armature, or stator in our case, affects the distribution
of the magnetic flux and produces a pulsating field these both cause
distortions of the voltage wave. In Fig. 14 and 14a is shown a voltage
wave having a very definite 23 harmonic which is most surely produced
by the tooth reaction on the field flux. In alternators having a few
slots and teeth per pole the movement of the slots across the field pro-
duces a pulsation of the magnetic reluctance of the field circuit and
this would cause a pulsation in the magnetic flux. The excitation in every
_Gase is kept constant. Therefore, a machine having s slots per pole,
the magnetic flux pulsates with 2s frequency.

Assuming that the pulsations followa simple sine law and have x" p
amplitude, the instantaneous flux interlinked with the armature coil is:

$= 9 cos (wt) (1 +k cos ( 2swr - r) )

The voltage generated is ;

e = -ndg
dt
then from the two above equations
@ = 2pifn™ g(sin (wt) (1 + k cos (2swt ~ r))
from trigonometry

2sinxcosy = sin(x + y) + sin (x - y)
Zoosxcoxy = sin (x + y) = sin (x - y]
6
Hence: e = 2pi tng (sinwt + x St sin ( (2841) wt - r + x ted sin
((2se1}wt - rv)

The pulsations of the magnetic flux due to the armature slots is
therefore the source of tw harmnics in the voltage curve of frequenoie s
28+] and 2s-] times the fundamental.

In the voltage wave as is shown in Fig. 14, we have the higher harmonic
present which is the twenty third. We have 12 slots per pole then from
the equation 2se-l, s = 12 then solving the equation we get 23 denoting the
235 hermnic using the first equation 28+1 and solving it we get a twenty
fifth harmonic, but by taking an oscillograph picture we find that we have
the twenty third.

Te wave shape of the electromotive force of an alternator is deter-
mined primarily by the distribution of the magnetic flux in its air-gap.
If the flux density in the air-gap varies sinusoidally with the di stance
measured along the circumference of the armature, the E.M.F. will be sinus-
oidal or (the wave will be a pure sine wave), assuming the armature con-
ductors to be symmetrically placed. Such a distribution of flux can be
approximated by properly shaping the field poles, but can never complete-
ly realized in a slotted armature. The effect of teeth is to produce
harmonics of relative high order, as evident by the shapp jags in the
resultant curves.

Taking the general outline of the curve we find that we have a curve
that resembles the ideal curves which illustrate the third harmonic. The
third harmonic is produced by the non-uniform distribution of the field
flux. TT remove this distortion and distribute the flux more evenly we
Champhered the sides of the pole faces so that they did not have the
shape of an arc, but such a shape that the alr-gap was increased 1/8 of an
inch at the edges and gradually decreasing to the aro or starting at 1/8

Of an inch and then decreasing to .04 of an inch air-gap. Then we again
?
assembled the alternator and then took pictures of the astion of the
current by the oscillograph and found that the higher harmonics had al-
most disappeared and that the third harmonic had disappeared entirely.
Then we found the higher harmonics also disappeared when the load was
applied (that is, a non-inductive load). Figures 16 and l6éa are pictures
taken of the oscillograms of the voltage waves. figure 16 is the picture
of the voltage wave as it is taken from the alternator, and l6a is the
picture as it is taken when the non-inductive load is applied, both phases
being loaded equally.

So far the discussion and pictures 9f wave forms have been either with
or without an inductive load so to see what action the inductive load
would have on the shape of the wave we connected a Soott transformer to
the alternator. We first took a picture of the voltage wave taken from
the alternator on the primary, the primary being the two phase connection
of the transformer, and found the wave form to be as is shown in Mg. 17.
In Fig. 17 note the points (a) and note the hump that is produced and at
(b) as light depression. Referring back to "ig. 16 you will note that
there is a similarity in both of these curves the depressions and the
hump appears in the same position only not so pronounced. In Mg. léa
these characteristias do not appear. Another element that will affect
the wave form is the variation in the permeability and the hysteresis with
the flux density in iron-clad circuits. This variation of the permeability
and hysteresis in the transformer together with that of the alternator is,
no doubt, the reason for this curve showing the vuriation so mich more
pronounced in fig. 17, that is shown in Fig. 16. To determine the real
effect of the conditions mentioned above a number of transformers with
different values of permeability and hysteresis should be connected to the
alternator and oscillograms taken of each condition and compared. In

Fig. 1%a, is a wave form of an inductive load taken off of the three phase
 
 
§
side of the Scott transformer. The shape of the curve is similar to those
in Ng. 16 and 17, but at the very peak of the cupwe note the amplitude of
the higher harmonics. In studying the curve it seems as if the higher
harmonics seem to have been Sransmitted thru the transformer but this is
not very likely to be the case. It is the characteristic wave of the
harmnics produced by a transformer that is connected in the line.

In the Figures 16 and 18a are curves of the inductive load with a
load on the three phase side of the Scott transformer. In Fig. 18 is the
wave of the transformer,on the two phase side note the similarity to th
wave of Fig. 17. The wave as is shown in Wig. 18a is the wave of the
transformer oonnected on the three phase side. Note how the characterist-
ics of the wave of Fig. 18 have been greatly magnified. ‘the reason for
this is probably the action of the transformer connected on the line.

Figure 19 is the oscillogram of the voltage wave taken of the two
phases at the same time. It is distinotly brought out that the voltages
are 90° apart. This is the real proof that the connection as made when
re-comnecting are correct.

The pole faces are made so that they are 70% of the pole pitch. ‘his
was done according to the statement of Mr. Smith of the Westinghouse
Company, to eliminate the harmonics. It would be interesting to have a
number of pole faces that could be inserted in the alternator and note
the effect of them on the wave form, form factor, and the other character-
istics of alternators. Take the rotor that we have and champher the pole
faces still more and see what effect it would have on the generated volt-
820.

It is well understood that small alternators cannot have revolving
poles as are supplied in large commercial alternators, but regardless of
this fact we designed a special rotor to fit this machine and rotated it

in the stator and found that possible am not practical because of the
aN md)

 
9
leakage of the field flux. It is true that salient pole pieces would be
very much better but due to the small size of the rotor this also would
not be practical.

When designing alternators that are to work as a separate unit and not
to be operated in parallel With other machines, no attention need to be
paid to the harmonics, as this was the general condition of the early
development of the electrical industry little attention was given to wave
forms. During recent years the central stations have increased enormously
and made it necessary to operate long-distance transmission lines of high
potentials. This maxes it necessary to study carefully all the factors
that may produce wave distortion.

If the wave form of two alternators operating in parallel are not of
the same shape, it is evident that for any instants during the time the
two waves are not equal the difference in the voltages cause cross-
currents to flow thru the two armatures. These cross currents will heat
up the armature and reduce the rating and the efficlency of the macnines
since the out-put or rating of well designed machines are based upon the
temperature rise.

This thesis has been valuable to the authors as it has broadened tneir
view point of the alternating current phenonima. It has also brought
Clearly before their mind some ‘f the factors that enter into the design
of alternating current machinery. It has helped us become familiar with
the oscillograph both in its operation and theory. We believe that the
oscillograph is an asset to tne teaching of alternating currents as the
therries that are browrnt out in the class-room Gan bs made mre clear
by its use, This osoilloxraph is not designed for soientific investi-
gation, but it is designed for a lecture demonstration of alternating

currents.

 
 

 

 

 

 

 
 

 

 

 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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MICHIGAN STATE LIBRARIES
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